The existence of bounded solutions of impulse systems with delay. (Russian) Zbl 0593.34066
Asymptotic integration of differential equations, Collect. sci. Works, Kiev 1985, 145-149 (1985).
[For the entire collection see Zbl 0575.00012.]
In this paper a nonlinear system of ordinary differential equations with delay is considered and the behaviour of the solutions of this system is investigated. It is presupposed that the corresponding averaged system has an asymptotically stable equilibrium position. Theorems for the existence of uniformly bounded solutions are proved. In the second part the existence of uniformly bounded solutions for the system considered is proved under the condition, that the corresponding averaged system has periodic solutions which are asymptotically orbitally stable for \(t\geq 0\).
In this paper a nonlinear system of ordinary differential equations with delay is considered and the behaviour of the solutions of this system is investigated. It is presupposed that the corresponding averaged system has an asymptotically stable equilibrium position. Theorems for the existence of uniformly bounded solutions are proved. In the second part the existence of uniformly bounded solutions for the system considered is proved under the condition, that the corresponding averaged system has periodic solutions which are asymptotically orbitally stable for \(t\geq 0\).
Reviewer: K.Barckow
MSC:
| 34K99 | Functional-differential equations (including equations with delayed, advanced or state-dependent argument) |
| 34A34 | Nonlinear ordinary differential equations and systems |
